establish the idendtity 11sint11sint2sec2 tSolution11sint1 1

establish the idendtity: 1/1-sint+1/1+sint=2sec² t

Solution

1/(1-sint+1)/( 1+sint) = 2sec² t

LHS 1/(1-sint) + 1/( 1+sint)

Taking Leas common denominator as (1+ sint)(1-sint)

(1 +sint + 1 -sint)/( 1+sint)( 1- sint)

2/( 1- sin^2t)

2/cos^2t

2sec^2t

RHS